AN ASYMPTOTICALLY PERIODIC SCHRÖDINGER EQUATION WITH INDEFINITE LINEAR PART

By Gongbao Li, A. Szulkin. 2002

178 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4d2a611bd9e31dcb87be9a1c381fc2849f1975f9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

The existence of a nontrivial solution to a nonlinear elliptic problem of linking type without the Ambrosetti-Rabinowitz condition (2011, unknown): “Although there is a linking theorem in [9] under the (C)c condition, it is not convenient for us to verify the assumptions which are required in the theorem.”
Periodic Nonlinear Schrödinger Equation with Application to Photonic Crystals (2004, background): “Some results in this direction can be found in [19], but the problem is still not well understood.”
Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations (2020, unknown): “[25,26] Let (X, ‖ · ‖) be a real Hilbert space with X = X− ⊕ X+ and X−⊥ X+, and let φ ∈ C1(X, R) of the form φ(u) = 1 2 (‖u+‖ − ‖u−‖)− ψ(u), u = u− + u+ ∈ X− ⊕ X+.”
Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms (2006, background): “In [18] it was proved that if (V0) and (N0)–(N2) hold then (NS) has at least one solution.”
New conditions on nonlinearity for a periodic Schrödinger equation having zero as spectrum (2014, background): “There is a large literature on existence and multiplicity results, for example, [3,5–7,9–11,15–17,19–23,27,28,30,32,33].”
On differential systems with strongly indefinite variational structure (2014, background): “It goes back to an idea of Li and Szulkin [21].”
New Super-quadratic Conditions on Ground State Solutions for Superlinear Schrödinger Equation (2014, unknown): “(SQ) was first introduced by Liu and Wang [12] and then was commonly used in recent papers, see [4, 5, 6, 8, 9, 13, 14, 16, 20, 18, 23].”
Multiple Solutions for Asymptotically Linear Elliptic Systems (2008, background): “8 in Li and Szulkin [20] for more details.”
A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations (2006, unknown): “It was also used in [29].”
Non-Nehari manifold method for asymptotically periodic Schrödinger equations (2014, unknown): “([12, 13]) Let X be a real Hilbert space with X = X− ⊕X+ and X−⊥ X+, and let φ ∈ C1(X,R) of the form φ(u) = 1 2 ( ‖u‖(2) − ‖u−‖2 ) − ψ(u), u = u− + u ∈ X− ⊕X.”